English

A note on simultaneous representation problem for interval and circular-arc graphs

Discrete Mathematics 2018-11-29 v2 Combinatorics

Abstract

In this short note, we show two NP-completeness results regarding the \emph{simultaneous representation problem}, introduced by Lubiw and Jampani. The simultaneous representation problem for a given class of intersection graphs asks if some kk graphs can be represented so that every vertex is represented by the same interval in each representation. We prove that it is NP-complete to decide this for the class of interval and circular-arc graphs in the case when kk is a part of the input and graphs are not in a sunflower position.

Keywords

Cite

@article{arxiv.1811.04062,
  title  = {A note on simultaneous representation problem for interval and circular-arc graphs},
  author = {Jan Bok and Nikola Jedličková},
  journal= {arXiv preprint arXiv:1811.04062},
  year   = {2018}
}

Comments

corrected figure

R2 v1 2026-06-23T05:10:48.750Z